Hey, I haven't posted here in a very long time! To answer the question about the moat, I had a look at a map from the 1880s (I'm afraid I cannot post a screenprint of it due to copyright but it is accessible through Digimap if you have it). The map shows there was indeed a moat alongside the lane although not in the location Len mentioned.
Because Yardley is hardly developed in the map it's hard to work out the bearings of the location but from my deductions, the moat was exactly where the car park and playgrounds for the recreation ground is today. The maps show it was there until at least the 1960s, although it looks like it was nearly all dried up by that point, and by the 1970s the car park and an electrical substation had been built on its site. Immediately west of it (where the rough patch of ground between the houses and entrance to the car park currently is) were four prefabs which were there at least into the 70s.
Now, I'm in my mid-20s so my memory obviously doesn't stretch that far but the 1970s map shows there was a post office in the middle of the recreation ground? I can only assume that this is the reason why the path from the northern car park is more like a road (deliveries) and the path from the southern car park is... well, a path! Where the two converge, the building was. And there was also a playground. Anyway, hope that solves the query!